For almost all known history of mankind, records exist of man having played games of chance. Various methods and objects have been used to introduce a true element of chance into the generation of an equal probability of some physical indication (reading) to manifest itself, within a range of equally possible probabilities. Perhaps, the best and simplest object used to generate such chance reading is a cube made of homogeneous material, referred to as die, which is thrown on a flat surface. Theoritically and for all practical purpose, such a cube has an equal chance to come to rest on either one of its six faces. The upper face thus fully exposed displays an indicium which constitutes the reading symbol. If all faces exhibit a different kind of symbol, each of such symbol has an equal probability to show up on the displayed face of the cube. It is one out of six. The probability number would be lower if the number of faces were made larger for each die. By its essence, a single cube fixes and limits the number of readings to six (six faces).
Other shapes of solid bodies exhibiting a larger number of faces exist and could prove more attractive as chance generator by offering a higher number of possible "chances". However, they must all have the typical characteristics inherent to a cube: (1) have equal and flat faces, (2) these flat faces must occupy the whole external surface of the body, (3) it must easily roll and always come to rest on one face, if unhampered, (4) each one of its faces must be easily readable without ambiguity, and (5) each and every face must have the same probability to come to rest when the body rolls unhindered on a flat surface. Generally speaking, and using standard dice as a model, this means that: (1) opposite faces must be parallel, (2) the angles made by the planes of any and all contiguous faces must be equal, (3) the perpendicular from the die center of gravity to each face must pass through that face center, (4) all faces have equal areas and identical shapes, and (5) all faces are adjacent to other faces along all of their periphery. A cube made of homogeneous material fulfills all of these conditions. These conditions are also fulfilled by two other regular polyhedra. There is only a total of 4 regular polyhedra in addition to the cube. The table below identifies them.
______________________________________ Name Number of Faces Face Shape ______________________________________ Tetrahedron 4 Triangular CUBE six SQUARE Octahedron 8 Triangular Dodecahedron 12 Pentagonal Isocahedron 20 Triangular ______________________________________
The tetrahedron has a pyramidal shape and does not qualify. The octahedron does not fulfill all of the conditions listed above and would offer little advantage over the cube. Only two regular geometric solid bodies are left and offer great possibilities: the dodecahedron and the isocahedron.
The dodecahedron, with twelve pentagonally shaped faces, is very attractive for use as a die, from all standpoints. It fulfills all conditions ideally and its faces are optimally shaped as compared to those of the isocahedron. The latter has twenty identical triangular faces. The number of its faces is larger than that of the dodecahedron, but a triangle is not ideally shaped to display a symbol.